Valence Bond Theory: Hybrid Orbitals, Sigma and Pi Bonds

A puzzle about carbon

Carbon's configuration is 1s² 2s² 2p². Its two 2s electrons are paired, and only the two 2p electrons are unpaired. Using simple orbital overlap, carbon should make two bonds at 90°. But methane, CH₄, has four identical C–H bonds at 109.5°. VSEPR predicts the shape correctly, but how do the orbitals manage it?

The answer comes from valence bond theory, developed by Linus Pauling and others in the 1930s: a covalent bond forms when orbitals on two atoms overlap and share a pair of electrons, and atoms can mix (hybridize) their orbitals to make new ones pointing in the right directions.

Hybrid orbitals

When carbon bonds, its 2s and 2p orbitals combine into new hybrid orbitals. The number of hybrid orbitals always equals the number of atomic orbitals mixed.

• sp³: one s + three p → four sp³ orbitals, pointing to the corners of a tetrahedron (109.5°). Used when the atom has 4 electron groups (CH₄, NH₃, H₂O, the carbons in ethane).
• sp²: one s + two p → three sp² orbitals in a plane at 120°; one p orbital is left unhybridized, at right angles to the plane. Used for 3 electron groups (BF₃, each carbon in ethene, C₂H₄).
• sp: one s + one p → two sp orbitals at 180°; two p orbitals are left over. Used for 2 electron groups (each carbon in ethyne, C₂H₂; the carbon in CO₂).

So the shortcut is: count the electron groups (as in VSEPR), and that tells you the hybridization. Lone pairs count as groups: the nitrogen in NH₃ is sp³.

(Many textbooks extend the idea to sp³d for five groups and sp³d² for six. Modern calculations suggest those molecules are better described in other ways, so this course uses hybridization mainly for 2, 3 and 4 groups.)

Sigma and pi bonds

• A sigma (σ) bond forms when orbitals overlap end to end, along the line between the two nuclei. Every single bond is a σ bond. σ bonds allow the atoms to rotate freely around the bond.
• A pi (π) bond forms when two parallel, unhybridized p orbitals overlap side by side, putting electron density above and below the bond axis.

Double bond = 1 σ + 1 π. Triple bond = 1 σ + 2 π.

In ethene, each carbon is sp². The sp² orbitals form σ bonds to two H atoms and to the other carbon; the leftover p orbitals overlap side by side to form the π bond. Because twisting one end would break that side-by-side overlap, there is no free rotation around a C=C double bond. That is why molecules such as cis-but-2-ene and trans-but-2-ene are different compounds, as you see in the Organic Chemistry unit.

In ethyne (HC≡CH), each carbon is sp. The two leftover p orbitals on each carbon form two π bonds at right angles to each other.

Delocalized π electrons

In some molecules, p orbitals on several neighbouring atoms overlap, and the π electrons spread over all of them. These electrons are delocalized. This is the orbital picture of resonance: in the nitrate ion and in benzene (C₆H₆), the π electrons belong to the whole ring or ion, so all the bonds are identical. In graphite, the π electrons are delocalized over entire sheets of carbon atoms, which is why graphite conducts electricity (see the lesson on types of solids).